Dropbox can be used to sync game save files. By using Dropbox you can jump back to previous savestates or recover your continue.sav at any time.
You just have to move your FasterThanLight folder to the Dropbox and create a symbolic link in its original location. Don't try to create a hard link, as this would only backup your current profile/savegame.

BitTorrent Sync can also be used to sync game save folders across operating systems. Just set up the respective folders to sync together via the same secret.

[syncthing.net SyncThing] can be used similarly to BitTorrent Sync, but provides more advanced options if so desired.